Angles of a Quadrilateral are in Ratio

The
four angles of a quadrilateral are in ratio then how to find the measure of
each angle of the quadrilateral. According to the angle sum property of
quadrilateral, we know that the sum of the angles of a quadrilateral is 360°.

Solved examples of angles of a quadrilateral are in ratio:

1. In a quadrilateral ABCD, the angles A, B, C, D are in the ratio 3 :
5 : 7 : 9. Find the measure of each angle of the quadrilateral.

Solution:

Let the common ratio be x.

Then the four angles of the quadrilateral
are 3x, 5x, 7x, 9x.

According to the angle sum property of
quadrilateral,

3x + 5x + 7x + 9x = 360

⇒ 24x = 360

⇒ x = 360/24

⇒ x = 15°

Therefore, measure of angle A 3x = 3 × 15 =
45°

Measure of angle B = 5x = 5 × 15 = 75°

Measure of angle C = 7x = 7 × 15 = 105°

Measure of angle D = 9x = 9 × 15 = 135°

Therefore, the four angles of the
quadrilateral are 45°, 75°, 105° and 135°.

2. The four
angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Find the angles.

Solution:

Let the measures of angles of the given quadrilateral be (2x)°, (3x)°, (5x)°
and (8x)°.

We know that the sum of the angles of a quadrilateral is 360°.

Therefore, 2x + 3x + 5x + 8x = 360

⇒ 18x = 360

⇒ x = 20.

So, the measures of angles of the given quadrilateral are

(2 × 20)°, (3 × 20)°, (5 × 20)° and (8 × 20)°

i.e., 40°, 60°, 100° and 160°.

3. The angles of a quadrilateral are in
ratio 1 : 2 : 3 : 4. Find the measure of each of the four angles.